Problem: Simplify the following expression and state the condition under which the simplification is valid: $t = \dfrac{y^2 + 5y}{y^2 + 6y + 5}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 + 5y}{y^2 + 6y + 5} = \dfrac{(y)(y + 5)}{(y + 1)(y + 5)} $ Notice that the term $(y + 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y + 5)$ gives: $t = \dfrac{y}{y + 1}$ Since we divided by $(y + 5)$, $y \neq -5$. $t = \dfrac{y}{y + 1}; \space y \neq -5$